Variable phaseplates for focus invariant optical systems

Abstract

Depth of focus can be enhanced with cubic phaseplates located at the exit pupil of an optical system without significant loss of resolution. The enhancement factor is proportional to the strength of the phaseplate. The digital image is inversely filtered. The stronger the phaseplate is the stronger the inverse filter function must be. This causes increasing noise for high spatial frequencies in the restored image. Therefore, an optimum strength of the cubic phaseplate has to be chosen for the respective situation. A variable phaseplate system has been realized and tested. The performance of the setup has been experimentally studied. Applications and practical aspects are discussed in particular regarding barcode readers.

Adaptive phase plates for optical encoding systems invariant to second-order aberrations

“…Moreover, we should point out that the formerly proposed methods based on lateral or diagonal translations usually give rise to a certain amount of unwanted lower order polynomials, the linear terms being the least relevant since they only lead to displacements of the image [12,13]. While digital processing can compensate for linear terms, when it comes to higher order terms compensation is not always possible and their effect would have to be analyzed separately.…”

“…Phase plates in the shape of R(r) * cos(nθ) can be effectively shaped in both refractive [12,16,19] and diffractive structures [22]. Besides, experimental generation of trefoil by rotation of only one pair of phase plates has been already reported for wavefront coding purposes [19] and the experimental generation of several Zernike aberrations has been experimentally demonstrated for correction of eye aberrations [16].…”

“…Therefore, the possibility of generating a controlled variable amount of phase would make it possible to adjust depth of field characteristics in an optimal way for each given situation within the same optical system. In order to achieve this, and based on the principles governing the generation of variable amounts of aberration explained above, Hellmuth et al [12] proposed and manufactured an adaptive phase plate where phase modulation can be adjusted by diagonally displacing two identical but opposite sign phase plates. Each plate can be considered as a linear combination of a 4th order polynomial, (x 4 + y 4 ) to control the cubic phase strength and a third order one, (x 3 + y 3 ), to change the focal length of the system.…”

Generation of spherical aberration with axially translating phase plates via extrinsic aberration

“…After the seminal work of Alvarez [1,2] a variety of papers have been published about the generation of aberration by the relative translation, or rotation of two complementary phase plates [3][4][5][6][7][8][9][10][11]. The basic theory is that the subtraction of the wavefront deformation introduced by one plate from the wavefront introduced by the other plate results in a particular type of aberration.…”

Effect of spherical aberration in trefoil phase plates on color wavefront coding

“…[5][6][7][8][9][10][11][12][13][14][15][16] Nevertheless, it has been shown that cubic and trefoil-shaped phases are most used to achieve high-quality images when spherical aberration, 10,11) astigmatism 14,15) and high orderaberrations 15) are also present in the system. WFC can be found in many different applications such as in ophthalmic optics, [15][16][17] iris recognition, 18,19) complexity reduction in optical systems, 20) control of thermal defocus in infrared systems, 21) barcode reading, 22) and microscopy, 23) among many others. The DOF in each application can be extended by a trefoil phase at the exit pupil of the optical system, and the trade-off between the DOF and the image resolution properties is dependent on the peak-to-valley value (strength) of the phase.…”